That pinging is a mystery.. and finding it's source seems far more important than tracking down the reason for the bad idle.
If there was no head-work compression ratio should be nearly the same... the head is not packed with carbon .. The new piston could be making contact with the head?
Rod bearing condition is unknown (to me) but if they're bad enough, who knows.. the noise would resemble a pinging or knocking.
But this noise happens only after it's warmed up and the result is the engine dies. I'd say its all related. Something is changing in the hot engine. Friction rises, a knocking noise develops, idle slows and the engine finally dies.
Something mechanical ain't right. I would not give up searching for it's source and continue the break-in as if everything were ok just yet.
Try one little test.
Remove the head, fasten the cylinder back down with a couple head bolts (use a stack of washers or tubing to "shorten" the head bolts).
Turn the flywheel so the piston rises and slightly passes over TDC. Then hit the piston crown with the heel of your hand. If you hear a distinctive "click" the rod bearings are probably gone. That could be the source of the pinging noise.